Question

State and verify Euler’s formula for a cube

Answer 1

Answer: V - E + F = 2; or, in words: the number of vertices, minus the number of edges, plus the number of faces, is equal to two. ... V - E + F = 12 - 30 + 20 = 32 - 30 = 2, as we expected. Euler's formula is true for the cube and the icosahedron.

Step-by-step explanation:

Answer 2

Euler's formula is related to the Faces, Edges and vertices of any polyhedron. 

Euler's formula is proved and verified for a cube

Explaination :-

Euler's Formula :

Vertices - Edges + Faces = 2

Cube has :

Vertices = 8

Faces = 6

Edges = 12

Formula :

→ V - E + F = 2

→ 8 - 12 + 6 = 2

→ 8 - 6 = 2

→ 2 = 2

$\therefore$LHS = RHS

$\therefore$Euler’s formula for a cube is verified.